1. Field of the Invention
The invention disclosed broadly relates to cryptography and more particularly relates to digital signature methods.
In contrast to conventional digital signature schemes, blind signature schemes allow the recipient to obtain signatures for messages that the signer does not learn. If the recipient can get only one signed message from each execution of the signing operation by the signer, then the blind signature scheme is called one-time, otherwise it is called many-time. Many-time blind signatures have been used to build untraceable tickets, called credentials. Such tickets can be issued by one organization and verified by another. Each customer uses different pseudonyms with each organization and a ticket is simply a blind signature for a customer pseudonym. The blinding property allows one to use different pseudonyms for issuing and showing a ticket. Even if all organizations collude, they cannot trace which tickets belong to which customers. One-time blind signatures have been used to build practical offline and online untraceable electronic cash schemes, where the issuing organizations are banks, the recipients are merchants and the tickets can be used only once. Most electronic cash schemes based on blind signatures use the one-time form, mainly to avoid the problem of multiple copies of the same electronic coin.
For offline untraceable electronic cash, double spending of coins should be detectable after the fact, so that double spenders are identifiable if and only if they use a coin more than once. This problem has been addressed by using restrictive one-time blind signatures. The customer's identity is embedded into her pseudonyms in such a way that it is revealed if and only if she double spends. A general blind signature scheme would allow a customer to also obtain coins for pseudonyms of other customers or for pseudonyms that are not assigned to anyone. In contrast, restrictive blind signature schemes guarantee that customers form their pseudonyms in a way that preserves the customer's identity, which the signer has encoded into each issued pseudonym.
A related application area is untraceable membership cards, which can be stored in palmtops, smartcards, etc. Owners may use their membership cards online or offline, arbitrarily often, and in an untraceable way, i.e., several uses of the same card cannot be linked by the respective verifiers. However, issuers of membership cards require that membership cards can be used only by their owners, not by other individuals, even if the owners wish to lend their membership cards away. Purely cryptographic solutions to this problem cannot exist because whether a membership card is actually used by its owner or someone else, is not distinguishable by cryptographic means. It has been suggested to use a wallet-with-observer architecture, where every user has a personal device (wallet) that is in part controlled by an implanted tamper resistant security module (observer). The observers can be equipped with a biometric sensor which is a sufficiently powerful hardware basis for the problem at hand. The prior art relies heavily on the tamper resistance of observers, because if an attacker breaks his observer he can not only lend his own membership cards to other individuals, but he can also forge new membership cards. Another approach relies on the tamper resistance of only observers with respect to transferability of membership cards. Attackers who break their observers can at most pool all the membership cards they already have, but cannot produce new ones. The approach includes a “cascade” signature scheme which has not been implemented.
What is needed in the prior art is a restrictive blind signature scheme that allows a recipient to obtain signatures for arbitrarily many (correctly formed) messages after only one interaction with the signer.